Finite Math Examples

$\frac{6}{25} b - \frac{1}{2} + \frac{11}{15} b - \frac{1}{5}$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{6}{25}$ and $b$ .

$\frac{6 b}{25} - \frac{1}{2} + \frac{11}{15} b - \frac{1}{5}$

Step 1.2

Combine $\frac{11}{15}$ and $b$ .

$\frac{6 b}{25} - \frac{1}{2} + \frac{11 b}{15} - \frac{1}{5}$

Step 2

To write $\frac{6 b}{25}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{6 b}{25} \cdot \frac{3}{3} + \frac{11 b}{15} - \frac{1}{2} - \frac{1}{5}$

Step 3

To write $\frac{11 b}{15}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6 b}{25} \cdot \frac{3}{3} + \frac{11 b}{15} \cdot \frac{5}{5} - \frac{1}{2} - \frac{1}{5}$

Step 4

Write each expression with a common denominator of $75$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{6 b}{25}$ by $\frac{3}{3}$ .

$\frac{6 b \cdot 3}{25 \cdot 3} + \frac{11 b}{15} \cdot \frac{5}{5} - \frac{1}{2} - \frac{1}{5}$

Step 4.2

Multiply $25$ by $3$ .

$\frac{6 b \cdot 3}{75} + \frac{11 b}{15} \cdot \frac{5}{5} - \frac{1}{2} - \frac{1}{5}$

Step 4.3

Multiply $\frac{11 b}{15}$ by $\frac{5}{5}$ .

$\frac{6 b \cdot 3}{75} + \frac{11 b \cdot 5}{15 \cdot 5} - \frac{1}{2} - \frac{1}{5}$

Step 4.4

Multiply $15$ by $5$ .

$\frac{6 b \cdot 3}{75} + \frac{11 b \cdot 5}{75} - \frac{1}{2} - \frac{1}{5}$

Step 5

Combine the numerators over the common denominator.

$\frac{6 b \cdot 3 + 11 b \cdot 5}{75} - \frac{1}{2} - \frac{1}{5}$

Step 6

Find the common denominator.

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Step 6.1

Multiply $\frac{6 b \cdot 3 + 11 b \cdot 5}{75}$ by $\frac{2}{2}$ .

$\frac{6 b \cdot 3 + 11 b \cdot 5}{75} \cdot \frac{2}{2} - \frac{1}{2} - \frac{1}{5}$

Step 6.2

Multiply $\frac{6 b \cdot 3 + 11 b \cdot 5}{75}$ by $\frac{2}{2}$ .

$\frac{(6 b \cdot 3 + 11 b \cdot 5) \cdot 2}{75 \cdot 2} - \frac{1}{2} - \frac{1}{5}$

Step 6.3

Multiply $\frac{1}{2}$ by $\frac{75}{75}$ .

$\frac{(6 b \cdot 3 + 11 b \cdot 5) \cdot 2}{75 \cdot 2} - (\frac{1}{2} \cdot \frac{75}{75}) - \frac{1}{5}$

Step 6.4

Multiply $\frac{1}{2}$ by $\frac{75}{75}$ .

$\frac{(6 b \cdot 3 + 11 b \cdot 5) \cdot 2}{75 \cdot 2} - \frac{75}{2 \cdot 75} - \frac{1}{5}$

Step 6.5

Multiply $\frac{1}{5}$ by $\frac{30}{30}$ .

$\frac{(6 b \cdot 3 + 11 b \cdot 5) \cdot 2}{75 \cdot 2} - \frac{75}{2 \cdot 75} - (\frac{1}{5} \cdot \frac{30}{30})$

Step 6.6

Multiply $\frac{1}{5}$ by $\frac{30}{30}$ .

$\frac{(6 b \cdot 3 + 11 b \cdot 5) \cdot 2}{75 \cdot 2} - \frac{75}{2 \cdot 75} - \frac{30}{5 \cdot 30}$

Step 6.7

Reorder the factors of $75 \cdot 2$ .

$\frac{(6 b \cdot 3 + 11 b \cdot 5) \cdot 2}{2 \cdot 75} - \frac{75}{2 \cdot 75} - \frac{30}{5 \cdot 30}$

Step 6.8

Multiply $2$ by $75$ .

$\frac{(6 b \cdot 3 + 11 b \cdot 5) \cdot 2}{150} - \frac{75}{2 \cdot 75} - \frac{30}{5 \cdot 30}$

Step 6.9

Multiply $2$ by $75$ .

$\frac{(6 b \cdot 3 + 11 b \cdot 5) \cdot 2}{150} - \frac{75}{150} - \frac{30}{5 \cdot 30}$

Step 6.10

Multiply $5$ by $30$ .

$\frac{(6 b \cdot 3 + 11 b \cdot 5) \cdot 2}{150} - \frac{75}{150} - \frac{30}{150}$

Step 7

Combine the numerators over the common denominator.

$\frac{(6 b \cdot 3 + 11 b \cdot 5) \cdot 2 - 75 - 30}{150}$

Step 8

Simplify each term.

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Step 8.1

Simplify each term.

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Step 8.1.1

Multiply $3$ by $6$ .

$\frac{(18 b + 11 b \cdot 5) \cdot 2 - 75 - 30}{150}$

Step 8.1.2

Multiply $5$ by $11$ .

$\frac{(18 b + 55 b) \cdot 2 - 75 - 30}{150}$

Step 8.2

Add $18 b$ and $55 b$ .

$\frac{73 b \cdot 2 - 75 - 30}{150}$

Step 8.3

Multiply $2$ by $73$ .

$\frac{146 b - 75 - 30}{150}$

Step 9

Subtract $30$ from $- 75$ .

$\frac{146 b - 105}{150}$